The evolution of growth trajectories and other complex quantitative characters.

Growth trajectories differ from many other quantitative characters in that they are characterized by a continuous function rather than by a finite number of discrete measurements. We review here recently developed methods for predicting the evolution of growth trajectories under the influence of natural or artificial selection. Using our method, analysis of genetic data from mice shows that the patterns of genetic variation arising from developmental processes impose constraints on evolution of growth trajectories. These constraints can be quantified to reveal the families of growth trajectories that can be produced by selection and those families that cannot. The data suggest there may be relatively few evolutionary degrees of freedom for growth trajectories despite the presence of abundant additive genetic variation to alter size and (or) growth rate at every age. The description of these constraints may be useful to both biologists who would like to determine the evolutionary options available to natural populations and to breeders who would like to alter growth trajectories to economically improve domesticated species. Our methods and conclusions can be generalized to other kinds of "infinite-dimensional" or complex characters, including morphological shapes and norms of reaction.